a.
To verify that the volume of the box is given by the function
a.
Answer to Problem 108E
The volume of the box is
Explanation of Solution
Given: An open box with locking tabs is to be made from a square piece of material 24 inches on a side. This is done by cutting equal squares from the corners and folding along the dashed lines.
Concept Used:
Volume of the box=
Calculation:
Length of the box =24- 2x .
Width of the box =24- 4x .
Height of the box = x .
Conclusion:
The volume of the box is
b.
To find the domain of the function V.
b.
Answer to Problem 108E
The domain of the function V is 0<x <6 cm.
Explanation of Solution
Given:
Given: An open box with locking tabs is to be made from a square piece of material 24 inches on a side. This is done by cutting equal squares from the corners and folding along the dashed lines.
Calculation:
Need to cut something, so x >0.
But cannot more than half the side length of the material. So also
Conclusion:
The domain of the function V is 0<x <6 cm.
c.
To sketch the graph of the function and estimate the value of x for which V(x) is maximum.
c.
Answer to Problem 108E
The maximum occurs at about
Explanation of Solution
Given:
Given: An open box with locking tabs is to be made from a square piece of material 24 inches on a side. This is done by cutting equal squares from the corners and folding along the dashed lines.
Calculation:
Using graphing utility below table that shows various box height as x and the corresponding volumes V as y.
Height x inches | Volume V |
0 | 0.00 |
1 | 440 |
2 | 640 |
3 | 648 |
4 | 512 |
5 | 280 |
6 | 0 |
The graph on above table data is shown below.
Where height as x -axis and the corresponding volumes V as y -axis .
Conclusion:
The maximum volume seems to occur between 5 and 7 cm.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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